Source signal separation involves recovering source signals from a composite signal, wherein the composite signal includes a mixture of the source signals. Source signal separation includes blind signal separation (BSS), for example. The separation is “blind” because it is often performed with limited information about the signals, the sources of the signals, and the effects that the propagation channel has on the signals.
An example is the familiar “cocktail party” effect when a person at a party is able to separate a single voice from a combination of all the voices in the room. Blind source separation is particularly applicable to cellular and personal wireless communications devices, where many frequency bands have become cluttered with numerous radio frequency emitters, often co-existing in the same spectrum. The problem of co-channel emitters is expected to only worsen in years to come with the development of low power, unlicensed wireless technologies such as Bluetooth and other personal area networks.
Three commonly used blind signal separation techniques are principal component analysis (PCA), independent component analysis (ICA) and singular value decomposition (SVD). PCA involves first and second moment statistics of the source signals, and is used when the signal-to-noise ratios of the source signals are high. Otherwise, ICA is used which involves PCA processing followed by third and fourth moment statistics of the source signals. As an alternative, SVD may be used to separate a source signal from the mixture of source signals based upon their eigenvalues.
Regardless of the blind signal separation technique that is applied, a plurality of sensors is used to receive different mixtures of the source signals from the various signal sources. Each sensor outputs a mixture of the source signals, which is a unique sum of the source signals. In general, both the channel coefficients and the original source signals are unknown to the receiver. The unique sums of signals are used to populate a mixing matrix. The appropriate blind signal separation technique is then applied to the mixing matrix for separating desired source signals from the mixture of source signals.
As an example, U.S. Pat. No. 6,799,170 discloses the separation of an independent source signal from a mixture of source signals using ICA. A plurality of sensors receive the mixture of source signals, and a processor takes samples of the mixture of source signals over time and stores each sample as a data vector to create a data set. Each sensor outputs a mixture of the source signals, which is a unique sum of the source signals. An ICA module performs an independent component analysis of the data vectors to separate an independent source signal from other signals in the mixture of source signals.
The sensors are spatially separated from one another, and the processor generates only one data vector for each respective sensor to create the data set. The '170 patent also discloses that the number of sensors N is equal to or greater than the number of sources M, i.e., N≧M for populating the data set. A problem with such an implementation is that as the number of sources M increases, then so does the number of sensors N. Small portable communications devices have little available volume for a large number of sensors N, and mounting the sensors on the outside of the communications devices is a problem for the users.
U.S. Pat. No. 6,931,362 discloses another method for separating signals using blind signal separation. The disclosed blind signal separation technique forms a mixing matrix with hybrid matrix-pencil adaptive array weights that minimize the mean squared errors due to both interference emitters and Gaussian noise. The hybrid weights maximize the signal to interference plus noise ratio. As with the '170 patent, the sensors are also spatially separated from one another, and the number of sensors N is equal to or greater than the number of sources M for populating the mixing matrix. Moreover, each sensor provides a single input to the mixing matrix resulting in a larger volume area for a portable communications device.
The rank of the mixing matrix thus determines how many signals can actually be separated. The larger the rank, the more signals that can be separated. A multipath signal is beneficial in that it can be used to populate the mixing matrix, as long as the multipath signal is independent in some measurable characteristic. Multipath occurs when a single data transmission encounters obstacles that cause it to split into multiple versions, each taking a different path to an intended receiver.
However, the symbols within a multipath signal may be time shifted so that when they reach the intended receiver, they may cancel or interfere with other received symbols. Alternatively, multipath may not even exist between the signal source and the intended receiver. As a consequence, the number of linearly independent signal sums received by the intended receiver for both of these cases may not be enough to populate the mixing matrix for signal separation.